Getting unique solution in data exchange

TL;DR: This work introduces a theoretical framework where the problem is transformed to an abduction problem, namely, definability abduction, and applies the framework to relational data exchange setting and solves the problem by pointing out minimal solutions according to a specific semantic minimality criterion.

Abstract: A schema mapping is a high-level specification in which the relationship between two database schemas is described. In data exchange, schema mappings are one-way mappings that describe which data can be brought from source data to target data. Therefore, given a source instance and a mapping, there might be more than one valid target instance. This fact causes many problems in query answering over target data for non-conjunctive queries. To make query answering feasible for all queries, we focus on a methodology for extending the original schema mapping to guarantee the uniqueness of target instance corresponding to a source instance. To this end, we introduce a theoretical framework where the problem is transformed to an abduction problem, namely, definability abduction. We apply the framework to relational data exchange setting and solve the problem by pointing out minimal solutions according to a specific semantic minimality criterion.